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Chapter 3: Problem 62

Explain how to write the negation of a conjunction.

Short Answer

Expert verified
The negation of conjunction \( P \land Q \) can be written according to De Morgan's laws as \( \sim P \lor \sim Q \), which means 'not P or not Q'

Step by step solution

01

Understand Conjunction and Negation

In formal logic, a conjunction is a compound sentence formed by using the word 'and' to join two simple sentences. The word 'and' is called a conjunction. For example, if you have two statements P and Q, the conjunction of P and Q would be written as \( P \land Q \). Negation is the logical operation that takes a statement P to another statement 'not P', denoted as \( \sim P \), which is true if and only if P is false
02

Fact About Negation of Conjunction

The negation of a conjunction of two statements is actually the disjunction (OR) of the negations of the statements. This is a direct application of De Morgan's laws which state these type of transformations.
03

Application of De Morgan鈥檚 laws

So, if you have the conjunction \( P \land Q \), then its negation would be \( \sim P \lor \sim Q \), meaning 'not P or not Q'

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Most popular questions from this chapter

Exercises 59-60 illustrate arguments that have appeared in cartoons. Each argument is restated below the cartoon. Translate the argument into symbolic form and then determine whether it is valid or invalid. If you do not know how to read, you cannot read War and Peace. If you cannot read War and Peace, then Leo Tolstoy will hate you. Therefore, if you do not know how to read, Leo Tolstoy will hate you.

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Translate each argument into symbolic form. Then determine whether the argument is valid or invalid. You may use a truth table or, if applicable, compare the argument's symbolic form to a standard valid or invalid form. (You can ignore differences in past, present, and future tense.) If I'm at the beach, then I swim in the ocean. If I swim in the ocean, then I feel refreshed. \(\therefore\) If I'm not at the beach, then I don't feel refreshed.
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